cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-6 of 6 results.

A377325 E.g.f. satisfies A(x) = 1 - log(1 - x*A(x))/A(x).

Original entry on oeis.org

1, 1, 1, 5, 28, 244, 2566, 33438, 508544, 8926944, 176989488, 3917823216, 95719041408, 2559130965312, 74312569125744, 2329169772108528, 78371469374088960, 2817744760964392704, 107807187260426164992, 4373419962377871956736, 187507942522161269068800
Offset: 0

Views

Author

Seiichi Manyama, Oct 24 2024

Keywords

Crossrefs

Programs

  • PARI
    a(n) = sum(k=0, (n+1)\2, (n-k)!/(n-2*k+1)!*abs(stirling(n, k, 1)));

Formula

a(n) = Sum_{k=0..floor((n+1)/2)} (n-k)!/(n-2*k+1)! * |Stirling1(n,k)|.

A377492 E.g.f. satisfies A(x) = 1/(1 + A(x) * log(1 - x*A(x)))^2.

Original entry on oeis.org

1, 2, 24, 562, 19974, 958468, 58085192, 4258862844, 366713780800, 36281317505040, 4056212559155664, 505750435243636944, 69586186789180895904, 10473322720889293098624, 1711744141030969885684320, 301912919501972279345773920, 57159241548809543158165770240
Offset: 0

Views

Author

Seiichi Manyama, Oct 29 2024

Keywords

Crossrefs

Programs

  • PARI
    a(n) = 2*sum(k=0, n, (2*n+3*k+1)!/(2*n+2*k+2)!*abs(stirling(n, k, 1)));

Formula

E.g.f.: B(x)^2, where B(x) is the e.g.f. of A377494.
a(n) = 2 * Sum_{k=0..n} (2*n+3*k+1)!/(2*n+2*k+2)! * |Stirling1(n,k)|.

A367160 E.g.f. satisfies A(x) = 1 - A(x)^3 * log(1 - x*A(x)).

Original entry on oeis.org

1, 1, 9, 161, 4412, 164024, 7721898, 440550102, 29548655696, 2278884869640, 198709176600696, 19331290511231280, 2075887738522499664, 243905626745780976144, 31125204862136659763040, 4287017279890868817295728, 633888142969750426274770944
Offset: 0

Views

Author

Seiichi Manyama, Nov 07 2023

Keywords

Crossrefs

Programs

  • PARI
    a(n) = sum(k=0, n, (n+3*k)!/(n+2*k+1)!*abs(stirling(n, k, 1)));

Formula

a(n) = Sum_{k=0..n} (n+3*k)!/(n+2*k+1)! * |Stirling1(n,k)|.

A377494 E.g.f. satisfies A(x) = 1/(1 + A(x)^2 * log(1 - x*A(x)^2)).

Original entry on oeis.org

1, 1, 11, 248, 8632, 408794, 24550512, 1788220664, 153204336480, 15097630639464, 1682516996213376, 209233809698022240, 28725012833286981456, 4315256340778010888688, 704140465438516958644512, 124020015235118786512297728, 23450965881108082875087150336, 4738390708952218941582313234176
Offset: 0

Views

Author

Seiichi Manyama, Oct 29 2024

Keywords

Crossrefs

Programs

  • PARI
    a(n) = sum(k=0, n, (2*n+3*k)!/(2*n+2*k+1)!*abs(stirling(n, k, 1)));

Formula

a(n) = Sum_{k=0..n} (2*n+3*k)!/(2*n+2*k+1)! * |Stirling1(n,k)|.

A377497 E.g.f. satisfies A(x) = 1/(1 + A(x)^3 * log(1 - x*A(x)^3)).

Original entry on oeis.org

1, 1, 15, 473, 23194, 1552084, 131908394, 13608546720, 1652258848656, 230829590868312, 36477894965606568, 6433858542834018240, 1252941162992516179776, 267027040073238416997024, 61819211233387513530840048, 15449035083850090935613775808, 4145148327496835979697002921216
Offset: 0

Views

Author

Seiichi Manyama, Oct 30 2024

Keywords

Crossrefs

Programs

  • PARI
    a(n) = sum(k=0, n, (3*n+4*k)!/(3*n+3*k+1)!*abs(stirling(n, k, 1)));

Formula

a(n) = Sum_{k=0..n} (3*n+4*k)!/(3*n+3*k+1)! * |Stirling1(n,k)|.

A377493 E.g.f. satisfies A(x) = 1/(1 + A(x) * log(1 - x*A(x)))^3.

Original entry on oeis.org

1, 3, 51, 1695, 85524, 5826402, 501281256, 52178851302, 6378309961152, 895845418408992, 142179729906910680, 25166131508370202776, 4915451890368514588032, 1050225776987234559170976, 243664809398578134394019712, 61008419406811276254021582384
Offset: 0

Views

Author

Seiichi Manyama, Oct 29 2024

Keywords

Crossrefs

Programs

  • PARI
    a(n) = 3*sum(k=0, n, (3*n+4*k+2)!/(3*n+3*k+3)!*abs(stirling(n, k, 1)));

Formula

E.g.f.: B(x)^3, where B(x) is the e.g.f. of A377497.
a(n) = 3 * Sum_{k=0..n} (3*n+4*k+2)!/(3*n+3*k+3)! * |Stirling1(n,k)|.
Showing 1-6 of 6 results.